Yes. There are solutions to all of these issues, but what often happens is these situations come about through the natural course of companies changing over time - different people managing accounts, different providers, etc. The happy path is easy, but the happy path is rarely the one we find ourselves walking down when we inherit a previously made decision.
1. Use "admin@domain.com"
2. Let the domain registration lapse
3. Someone else registers the domain and now can't create an AWS account.
Rare but not impossible.